Hello aspirant
As per now, no commencement date has been released for interior design course. Also every college begins around a different time period so there's no particular date.
So it basically depends on the college you have applied for and if you have cleared their aptitude test and selection process. As of now, there are some collges whose entrance exams are still about to take place in coming months and some whose results will be declared soon.
If you can let me know, which college you are looking for, i can help you with the knowledge regarding their entrance dates, application forms, etc. And after you have cleared the selection process, the college will let you know the starting date of your course. Usually the course starts around July- August-september
hope this helps